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A novel and fast three-phase load flow algorithm for unbalanced radial distribution systems is proposed in this paper. The proposed method uses branch voltages as state variables and employs the Newton-Raphson (NR) algorithm to solve the load flow problem. By utilizing branch voltages as state variables, a constant Jacobian matrix can be obtained, and a building algorithm for Jacobian matrix is then developed from the observation of the constant Jacobian matrix. A solution technique, which takes the network structure into account to avoid the time-consuming lower and upper triangular (LU) factorization, is also developed. Since the factorization procedure can be avoided, the proposed method can save computation time. For any power system equipment, if its equivalent current injection or admittance matrix can be obtained, it can be integrated into the proposed method. Test results demonstrate that by integrating the Jacobian building algorithm and efficient solution technique, the proposed method is an effective three-phase load flow method and has great potential for real-time use.